Role of thrust and drag clarified for swimming microorganisms

A snapshot of a linear chain of three little spheres and a big sphere. The individual spheres perform relative oscillatory motion along the axis. The fluid converts the internal relative motion into motion of the center of mass. Credit: Felderhof

For years, B. Ubbo Felderhof, a professor at the Institute for Theoretical Physics at Germany's RWTH Aachen University, has explored the mechanisms that fish and microorganisms rely on to propel themselves. Flying birds and insects face similar challenges propelling themselves, but without the luxury of buoyancy these creatures also contend with overcoming gravity to stay aloft.

Over 20 years ago, Felderhof was studying the theory behind the "swimming" of microorganisms, described by the friction interactions between the microbodies and their surrounding fluid. Because of the small mass of many such microorganisms like bacteria, such inertial forces could be neglected in the description. For slightly larger organisms, however, this was not the case.

Felderhof has since created mechanical models to more fully develop the theory, consisting of linear chains of spheres connected by springs and immersed in fluid. Here he took into account that the interaction with the fluid involves both friction and inertia, since the effect of mass can't be neglected for these larger structures.

As Felderhof now reports in Physics of Fluids, he's just pushed this work even further by addressing what happens in the case of adding one sphere to the chain that's much larger than the other spheres.

Felderhof studies structures of spheres because the effect of friction and fluid inertia on the motion of a single sphere is fairly well known. With multiple spheres, however, the picture is more complex and has to take into account positions and orientations. "For several spheres, there is the complication of hydrodynamic interactions due to interference of flow patterns," he said. "These hydrodynamic interactions depend on the relative positions of sphere centers."

If the relative positions of the spheres are varied periodically by applying an oscillating force on each of them, with the constraint that the total net force vanishes at any time, the system still sees movement. "In spite of the latter constraint, the set of spheres in general performs a net motion, which is called 'swimming,'" Felderhof said.

A mathematical formulation allows finding the optimum stroke—the combined applied forces—that yields the maximum average speed for a given power.

For this new work, Felderhof explored a linear chain of spheres with one big, passive sphere, meaning the applied force on that sphere vanishes. "The big sphere is called the 'cargo,'" he said. "Think of it as a large body with small moving appendages, or of a boat being pushed or pulled by a small propeller."

His work provides an important conceptual clarification of flow theory. "In popular explanations of swimming and flying, we're told that speed is achieved by a balance of thrust and drag," Felderhof said. "My model calculations, however, show that the mean thrust and drag both vanish when averaged over a period. The effect is more subtle. Interactions of body and fluid are such that periodic shape deformations of the body lead to a net motion relative to the fluid, even though the net thrust vanishes."

Much of the previous work on swimming has concentrated on either the friction-dominated limit, valid for microorganisms, or on the inertia-dominated limit, valid for large animals. "In my model, both friction and inertia play a role so that swimming can be studied in the intermediate regime, where both effects are important," he said.

In terms of applications, the swimming linear chain model is particularly useful because of its slender structure and ability to travel through narrow tubes, such human veins.

"Biologists have already considered the possibility of drug transport via such means," Felderhof said. "And now we've developed a mathematical model that allows optimization of deformations of the body, which leads to maximum speed for given power. This method isn't limited to linear chains, so we can envision applying it to more complicated structures in future work."

First, Felderhof points out that it is important to validate the model by comparison with computer simulations and subsequent experiments, which is beyond his focus, so he hopes other researchers will pursue it.

"Friction and inertia aren't the only effects that can lead to swimming," Felderhof said. "Flapping leads to vortex shedding and possibly a 'street' of vortices. This effect is absent from my model, but may be essential for the swimming of some fish and for flying birds. It will be of value to establish the relative importance of friction, inertia, and vortex shedding, but at present I don't see how this can be accomplished in analytical theory. Again, computer simulation would be helpful."

Related Stories

Scale plays a major role in locomotion. Swimming microorganisms, such as bacteria and spermatozoa, are subjected to relatively small inertial forces compared to the viscous forces exerted by the surrounding fluid. Such low-level ...

Inspired by micro-scale motions of nature, a group of researchers at the Indian Institute of Technology Madras and the Institute of Mathematical Sciences, in Chennai, India, has developed a new design for transporting colloidal ...

It's a common swimming pool game: Force a buoyant ball underwater and let it go. The ball springs to the surface and jumps into the air. But, submerge the ball deeper underwater and the effect is often disappointing. Contrary ...

The scientific community uses spheres for all sorts of things—artificial limbs, cars, molecular chemistry—but there's always a little uncertainty when this geometric shape is introduced into an experiment. While spheres ...

Researchers from CNRS, Inserm, and Université Joseph Fourier - Grenoble have developed a particularly simple model that reproduces the swimming mechanism of amoebas. They show that, by changing shape, these single cell organisms ...

New research findings are yielding insights into the physics behind the swimming behavior of bacteria and spermatozoa that could lead to a better understanding of the mechanisms affecting fertility and formation of bacterial ...

Recommended for you

A team of scientists has detected a hidden state of electronic order in a layered material containing lanthanum, barium, copper, and oxygen (LBCO). When cooled to a certain temperature and with certain concentrations of barium, ...

A team of researchers from the U.S., New Zealand and Norway has used computer simulations to predict several characteristics of the heaviest element, oganesson. In their paper published in the journal Physical Review Letters, ...

Researchers at the Center for Quantum Nanoscience within the Institute for Basic Science (IBS) have made a major breakthrough in controlling the quantum properties of single atoms. In an international collaboration with IBM ...

A team of researchers led by the Department of Energy's Oak Ridge National Laboratory has demonstrated a new method for splitting light beams into their frequency modes. The scientists can then choose the frequencies they ...

A team of researchers from several institutions in Japan has described a physical system that can be described as existing above "absolute hot" and also below absolute zero. In their paper published in the journal Physical ...

If they exist, axions, among the candidates for dark matter particles, could interact with the matter comprising the universe, but at a much weaker extent than previously theorized. New, rigorous constraints on the properties ...

0 comments

Please sign in to add a comment.
Registration is free, and takes less than a minute.
Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.